Standard form of the equation of parabola

[jOANIE]

Homework Statement

Write the equation in standard form for the parabola with an axis of symmetry y=0 and focus(-5,0).

Homework Equations

I think ax^2+bx+c. Also maybe x = -b/2a. But I don't know how to apply these.

The Attempt at a Solution

I know that focus and vertex lie on axis of symmetry and that directrix ane axis of symmetry are perpendicular to each other.

If you could give me a similar example worked out, I would be able to do this one. Thanks.

 

[Mark44]

Homework Statement

Write the equation in standard form for the parabola with an axis of symmetry y=0 and focus(-5,0).

Homework Equations

I think ax^2+bx+c.

I think not. First off, that's not an equation. Second, the axis of symmetry is the line y = 0 (the x-axis). This means that the equation will be x = ay^2 + by + c.

Also maybe x = -b/2a. But I don't know how to apply these.

x = -b/(2a) isn't the equation of a parabola; it gives you the x-coordinate of the vertex for a parabola that opens up or down. Your parabola opens left or right.

The Attempt at a Solution

I know that focus and vertex lie on axis of symmetry and that directrix ane axis of symmetry are perpendicular to each other.

If you could give me a similar example worked out, I would be able to do this one. Thanks.

Based on the information you provided, there are an infinite number of parabolas that satisfy these conditions. Aren't there any examples showing how to do this in your textbook?

 

[jOANIE]

Hello--Thanks for responding. I cannot find an example like this one in my book. Could you give me any hints on how to begin this problem? I am completely self-taught in math and am trying to understand conics, which I have not attempted before. I am also good at following examples and, actually, learn quite a bit from them.

 

[Mark44]

OK, what's the example that seems the closest? Are there any examples where you're supposed to find the equation of a parabola of any kind? Maybe we can help you make some connections.